pgon = polyshape([0 0 1 1],[1 0 0 1]);
figure(4)
plot(pgon)

pgon1 = nsidedpoly(6);
pgon2 = nsidedpoly(6,'Center',[5 0],'SideLength',3);
figure(4)
plot([pgon1 pgon2])
axis equal

L = linspace(0,2.*pi,100);
xv = 1.2*cos(L)';
yv = 1.2*sin(L)'; 
xx=1.1*cos(L)';
yy=1.1*sin(L)';
AA=polyshape(xv,yv);
AAA=polyshape(xx,yy);

plot(AA);
hold on;
plot(AAA);
title(['Area = ' num2str(A)])
axis image

A = polyarea(xv,yv)  %计算面积

clc,clear all;
L = linspace(0,2.*pi,100);
xv1 = 1.2*cos(L)';
yv1 = 1.2*sin(L)'; 
xv2=0.4*cos(L)';
yv2=0.4*sin(L)';

Round1=polyshape(xv1,yv1);
Round2=polyshape(xv2,yv2);
Round1Area = polyarea(xv1,yv1)
Round2Area = polyarea(xv2,yv2)

rng default  %恢复matlab启动时默认的全局随机流
xq = randn(250,1);  %随机生成250个正态分布点
yq = randn(250,1);  %随机生成250个正态分布点

in = inpolygon(xq,yq,xv1,yv1);  % numel(xq(in))查看在几何体内部的数量
figure(4)
plot(Round1); %画第一个圆
hold on;
plot(Round2); %画第二个圆
plot(xq(in),yq(in),'r+') % 标记在内部的点
plot(xq(~in),yq(~in),'bo') % 标记在外部的点
hold off
title(['Area1,Area2 = ' num2str(Round1Area),num2str(Round2Area)])
axis equal
axis image

axes('xlim',[0 10],'ylim',[0 10])
a=[1 1 2 2];
b=[3 4 5 6];
c=[1 1 3 3];
figure
rectangle('position',a,'EdgeColor', 'r');
rectangle('position',b,'EdgeColor', 'b');
rectangle('position',c,'EdgeColor', 'k');

area_ab = rectint(a,b)
area_ac = rectint(a,c)

a=1;b=1.5;d=0:360;
x=a*cosd(d);
y=b*sind(d);
figure(1),cla
patch(x+0.6,y+0.2,'b','edgecolor','none','facealpha',0.15);%不透明度0.15
patch(x-0.6,y-0.2,'b','edgecolor','none','facealpha',0.15);%不透明度0.15
patch(x-0.2,y+0.9,'b','edgecolor','none','facealpha',0.15);%不透明度0.15
patch(x+0.2,y-0.9,'b','edgecolor','none','facealpha',0.15);%不透明度0.15
axis equal
box on;
set(gcf,'color','w');

v1 = [2 4; 2 8; 8 4];
f1 = [1 2 3];
figure
patch('Faces',f1,'Vertices',v1,'FaceColor','red','FaceAlpha',.3);

v2 = [2 4; 2 8; 8 8];
f2 = [1 2 3];
patch('Faces',f2,'Vertices',v2,'FaceColor','blue','FaceAlpha',.5);

x = gallery('uniformdata',3000,1,1);
y = gallery('uniformdata',3000,1,10);

plot(x,y,'k.')
xlim([-0.3 1.2])
ylim([-0.3 1.2])
k = boundary(x,y); %返回一个表示包围点 (x,y) 的单个相容二维边界的点索引向量。收缩因子为1
hold on;
line(x(k),y(k),'color','b'); 

j = boundary(x,y,0.01); %收缩因子为0.1  最大为1 越大包裹性越紧
line(x(j),y(j),'color','r');

[~, vol] = boundary(x,y);  %包围点形成的形状的体积 或 面积
axis equal;
vol %返回 包围的体积或者面积

P = gallery('uniformdata',30,3,5);
subplot(1,2,1);
plot3(P(:,1),P(:,2),P(:,3),'.','MarkerSize',10)
axis equal;
grid on
k = boundary(P);
hold on
subplot(1,2,2);
trisurf(k,P(:,1),P(:,2),P(:,3),'Facecolor','red','FaceAlpha',0.1)  %收缩因子默认0
[~, vol] = boundary(P);  %包围点形成的形状的体积
axis equal;
vol %体积

xx = -1:.05:1;
yy = abs(sqrt(xx));
[x,y] = pol2cart(xx,yy);
k = convhull(x,y);
plot(x(k),y(k),'r-',x,y,'bo')

th = (pi/12:pi/12:2*pi)';
x1 = [reshape(cos(th)*(1:5), numel(cos(th)*(1:5)),1); 0];
y1 = [reshape(sin(th)*(1:5), numel(sin(th)*(1:5)),1); 0];
x = [x1; x1+15];
y = [y1; y1];
subplot(1,2,1)
plot(x,y,'.')
axis equal
subplot(1,2,2)
shp = alphaShape(x,y); %默认 alpha 半径可生成带不规则边界的 alpha 形状。
shp.Alpha = 2.5; % 要更好地捕获点集边界，请尝试更大的alpha 半径。
plot(shp)
axis equal

P = gallery('uniformdata',[30 2],0);
DT = delaunayTriangulation(P);
IC = incenter(DT);
triplot(DT) %绘制 Delaunay 三角剖分 
hold on
plot(IC(:,1),IC(:,2),'*r')